OF THE CRITICAL VELOCITY OF WATER WITH TEMPERATURE. 
55 
Hence 
1 dp 7 
p dr 1 — 7 T 
a. + 2/3t 
1 + tZT + /3 t" 
cIt (l '— n) ' f/r.T''' 
1 — JT 
For stream-line motion n = 1, and the values of a and /S taken from Poiseuille’s 
formula are 
a =-03368, ^=-000221. 
The value of y for -water is approximately ‘00048, and hence the second term is 
never important, and the first term is oiily important where cIt is la,rge (and the 
term a 2^t is not small). 
For stream-line motion the correction for a difference of F at 10° C. is 
approximately ‘028, while at 50° C. it is '017. 
The observations recorded in the table, corrected to a mean temperature, are 
plotted in fig. 4. [tThe diagram shows the logarithmic homologues for streamdine 
motion in the pipe at ten different temperatures between 4° C. and 50° C., and 
these are represented by a series of straight lines equally inclined to the axes of 
co-ordinates. The mean temperatures to which the observations have been reduced 
are as follows :— 
Experiments. 
Reduced to a mean tem¬ 
perature Centigrade of 
Corresponding lines on 
«g. 4. 
1 to 8 
o 
4-5 
1 
9 „ 15 
11-2 
2 
16 „ 2.3 
16-8 
3 
24 „ 32 
18-1 
4 
33 ., 39 
27-2 
5 
40 „ 43 
31'1 
6 
44 „ 50 
34-4 
7 
51 „ 57 
37'8 
8 
58 ,, 64 
42-3 
9 
65 „ 71 
49-3 
10 
These lines were] found to agree closely with the formula 
where r is the radius of the pipe, and p .2 the pressures at the ends, I the length oi 
pipe, aird [x is the coefficient of viscosity. 
* Corrected Nov. 14, 1902, as pointed out by the Referee, 
t Added Nov. 14, 1902. 
t Loc. (it. ante (p. 48). 
